Does getting a good night's sleep on a regular basis have a positive affect on academic achievement? Sleep plays an important role in learning and memory so it seems reasonable to conjecture that nightly sleep duration is an important factor in academic success.

To examine this conjecture 139 undergraduates from a large public university were monitored during the Spring term of a recent academic year. Their sleep was tracked during the term using the Fitbit Flex 2 and their term GPA's were provided by the university registrar. The data is shown in this Excel file Sleep and GPA; for each student the average hours of sleep per night during the Spring term and the Spring term GPA were recorded.

Question 1. Determine the slope b₁ and intercept b₀ of the least squares prediction line= b₀ + b₁x where the explanatory variable x is average hours of sleep per night and the response variable y is term GPA.

______ slope (use 4 decimal places) ________ intercept

Question 2. What is the predicted term GPA of a student that gets an average of 6 hours of sleep per night.

____ (use 2 decimal places)

Question 3. What is the change in term GPA for each additional half-hour of average sleep time per night?

A decrease of 0.1234

An increase of 0.7404

An increase of 0.1234

An increase of 1.6394

An increase of 0.02468

An increase of 0.8197